Energy-Momentum Tensor of Field Fluctuations in Massive Chaotic Inflation

TL;DR

This paper analyzes the energy-momentum tensor of inflaton fluctuations during chaotic inflation, introducing a novel approximation method that reveals how quantum effects evolve and depend on inflation duration.

Contribution

It presents a new analytic approximation for inflaton fluctuations during slow-roll inflation and demonstrates its validity through numerical verification, advancing understanding of quantum effects in inflation.

Findings

The spectrum of inflaton fluctuations is scale invariant during slow-roll.

The renormalized energy-momentum tensor is conserved and matches known results in de Sitter space.

Quantum production of light scalar fields depends on the inflation duration and exceeds standard de Sitter estimates.

Abstract

We study the renormalized energy-momentum tensor (EMT) of the inflaton fluctuations in rigid space-times during the slow-rollover regime for chaotic inflation with a mass term. We use dimensional regularization with adiabatic subtraction and introduce a novel analytic approximation for the inflaton fluctuations which is valid during the slow-rollover regime. Using this approximation we find a scale invariant spectrum for the inflaton fluctuations in a rigid space-time, and we confirm this result by numerical methods. The resulting renormalized EMT is covariantly conserved and agrees with the Allen-Folacci result in the de Sitter limit, when the expansion is exactly linearly exponential in time. We analytically show that the EMT tensor of the inflaton fluctuations grows initially in time, but saturates to the value H^2 H(0)^2, where H is the Hubble parameter and H(0) is its value when inflation has started. This result also implies that the quantum production of light scalar fields (with mass smaller or equal to the inflaton mass) in this model of chaotic inflation depends on the duration of inflation and is larger than the usual result extrapolated from the de Sitter result.